The present invention relates to numerical techniques for modeling and solving complex system equations through the use of a finite element model and more particularly to a method for incorporating boundary conditions into a finite element model.
Finite element analysis is a computerized method widely used in industry to model and solve engineering problems relating to complex systems. A finite element model is generating by reducing the system, or domain, into a number of discretized units typically referred to as finite elements. Once reduced, the domain can be represented by a system of equations that are solved, typically by computer, to predict the response of the domain to various external influences. Finite element analysis is used in a variety of applications including solid mechanics, fluid mechanics, biomechanics, heat transfer, geomechanics, aeromechanics, coupled systems, chemical reactions, acoustics, and electric and magnetic fields.
Perhaps the most common use of finite element analysis is in the field of solid mechanics where it is used to analyze structural problems. Finite element analysis software adapted for use with solid mechanics is available from a wide variety of commercial suppliers. Finite element analysis begins by using finite element software to generating a finite element model of the system. In this model, the component is reduced into a number of finite elements. The finite element reduction is fixed to "ground" at more or more locations to simulate attachment of the component to an interface structure. In the finite element model, "ground" represents a perfectly rigid structure that will not flex or move under a load. A simulated load or other influence is applied to the system and the resulting effect is analyzed using conventional mathematical methodologies. This method is well suited when the designed component is to interface with a structure that is, like ground, perfectly rigid. In many applications, however, the structure with which the component is to interface will not have such characteristics. This poses a significant problem because the rigidity of the interface structure affects the natural frequencies of any components attached thereto. For example, automobile engine mounting bosses do not have the same rigidity characteristics as ground. Therefore, engine brackets and similar components will exhibit different natural frequencies when mounted to the engine than when modeled using conventional finite element analysis.
One method for addressing this problem is to design the component using conventional finite element analysis, manufacture a prototype based on this design, and then physically determine the natural frequencies of the prototype attached to the interface structure (i.e. the engine). Once the actual natural frequencies are determined, the boundary conditions of the finite element model are adjusted using a trial and error method until an acceptable correlation with the measured frequencies is achieved. This process is extremely time consuming and CPU intensive because it requires the design and testing of an initial prototype as well as repeated adjustment and resolution of the system equations.